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Various Differential Equations Topics 

This page contains several differential equations topics that are not discussed in detail but we provide some overview information and maybe a video or two, as well as links to other pages with more indepth information, if we have any. We may expand these topics as a later date but, for now, this will get you started. Here is a list of topics on this page. 
Basic Topics  Advanced Topics  

Existence and Uniqueness 
Here is a discussion of the Lipschitz condition, which is related to whether a differential equation has a solution and, if so, whether the solution is unique.
Dr Chris Tisdell  Lipschitz Condition  
Boundary Value Problems 
Here are three videos related to boundary value problems.
Dr Chris Tisdell  advanced differential equations and boundary value problems  
Dr Chris Tisdell  how to determine eigenvalues of a boundary value problem  
Dr Chris Tisdell  D'alembert's approach for boundary value problems  
Euler's Method 
MIT OCW  Title: Lec 2  MIT 18.03 Differential Equations, Spring 2006;  
Inhomogeneous ODEs 
MIT OCW  Title: Lec 13  MIT 18.03 Differential Equations, Spring 2006  
Resonance 
MIT OCW  Title: Lec 14  MIT 18.03 Differential Equations, Spring 2006  
Partial Differential Equations 
Here are two videos related to pde's using the method of characteristics. We highly recommend this guy's videos.
Dr Chris Tisdell  This first video introduces the topic and gives some examples.  
Dr Chris Tisdell  This second video gives more detail and another example.  
Linear Systems 
Dr Chris Tisdell  How to solve systems of ODEs without matrices  
Dr Chris Tisdell  Basic solution form to systems of differential equations  
Dr Chris Tisdell  How to solve systems of differential equations  
PatrickJMT  Homogeneous Systems of Linear Equations  Trivial and Nontrivial Solutions, Part 1  
PatrickJMT  Homogeneous Systems of Linear Equations  Trivial and Nontrivial Solutions, Part 2  